Scaling Laws for Overlaid Wireless Networks: A Cognitive Radio Network vs. a Primary Network

We study the scaling laws for the throughputs of two coexisting wireless networks that operate in the same geographic region. The primary network consists of Poisson distributed legacy users of density n, and the secondary network consists of Poisson distributed cognitive users of density m, with m > n. The primary users have a higher priority to access the spectrum without particular considerations for the secondary users, while the secondary users have to act conservatively in order to limit interference to the primary users. With a practical assumption that the secondary users only know the locations of the primary transmitters, we show that both networks can achieve the same throughput scaling law as a stand-alone wireless network if proper transmission schemes are deployed, where a finite throughput is achievable for each individual secondary user (i.e., zero outage) with high probability.